Wing Lift and Drag Calculator With Stall Speed and Mach Number

Lift, drag, stall speed and Mach number from the speed and wing data.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Enter the speed, the air density, the wing area, the lift and drag coefficients and the weight. The calculator gives the dynamic pressure, the lift and the drag, the lift to drag ratio and the stall speed, which is the lowest speed at which the wing can still lift the weight.

From the air temperature it works out the speed of sound and the Mach number, and above Mach 1 the angle of the shock wave. It tells you which regime applies: below about Mach 0.3 the simple equations are accurate; transonic, supersonic and hypersonic flight need other methods.

Use it for light aircraft and drones, fans and propeller blades, and for physics and aerodynamics problems.

Formulas used

  • L = \tfrac{1}{2}\rho v^2 S C_L
  • D = \tfrac{1}{2}\rho v^2 S C_D
  • M = \frac{v}{a},\ \sin\mu = \frac{1}{M}

Worked example

With the default numbers in the calculator above:

  1. Dynamic pressure: 3001.25 Pa
  2. Lift: 57624.00 N (57.62 kN)
  3. Drag: 2401.00 N
  4. Lift to drag ratio: 24.00
  5. Weight and the lift compared with it: 9810.00 N, lift is 5.874 times the weight
  6. Stall speed (lift equals weight at the maximum lift coefficient): 23.58 m/s (84.90 km/h)
  7. Speed of sound at this temperature: 340.29 m/s
  8. Mach number: 0.2057

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

Why does stall speed go up at altitude?

The air is thinner, so the wing needs more speed to make the same lift. The true airspeed at stall rises as the density falls.

What is the Mach angle?

Above Mach 1, the angle of the cone of the shock wave, whose sine is 1 divided by the Mach number.

Are these accurate near Mach 1?

No. Near the speed of sound shock waves form and the coefficients change a lot, so the simple equations do not apply.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Anderson, Fundamentals of Aerodynamics; Anderson, Introduction to Flight.

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